Traverse That Closes 1:6,800 and a Party Chief With a Compass Rule
Your crew ran a five-sided closed traverse around a 40-acre parcel in Nye County, beginning and closing on two published NGS monuments in the Nevada State Plane Coordinate System (NAD83, Nevada East, U.S. survey feet). Distances were measured with a total station in ground units and then reduced to grid; the field book shows the combined scale factor was applied, but the party chief cannot say whether it was multiplied or divided. The angular closure is 18 seconds, inside your firm's 20 root n second tolerance. The linear closure is 0.42 foot over a perimeter of 2,860 feet. The record of survey must close on the two NGS monuments at 1:10,000 or better. The party chief says, 'Just adjust it out with the compass rule, nobody will ever know.' The client wants a signed map, and the monuments are a three-hour drive away.
1. Compute the closure ratio and the part-per-million error, and state whether the requirement is met. What does the combination of a good angle closure and a poor linear closure tell you?
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Closure ratio: 0.42 ft / 2,860 ft = 1/6,810, reported as about 1:6,800. The requirement is 1:10,000, so the traverse fails.
ppm: (0.42/2,860) x 1,000,000 = 147 ppm. At 147 ppm, a 1,000-foot line carries about 0.15 ft of error, which is enough to matter for monument positions and boundary retracement.
The diagnostic split matters more than the number. With five angles, the allowable angular misclosure is 20 root 5 = 44.7 seconds; you achieved 18 seconds. Angles are clean, so the error is essentially all in the distances. That points away from random centering and pointing noise (which would degrade the angles too) and toward either a systematic distance error applied to every leg, or a blunder in one leg. A systematic error of 147 ppm is squarely in the range of a combined scale factor being multiplied when it should have been divided, doubled, or omitted for this area. A blunder, by contrast, concentrates in one direction.
2. Diagnose the likely causes and explain how you would distinguish them in the field and in the reduction.
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Systematic scale error. Re-reduce the raw ground distances with the combined scale factor applied correctly and compare the resulting grid distances with the published NGS coordinates. Check one leg by an independent method, such as a second NGS pair or a published baseline. If the sign is wrong, the correction reverses in every leg proportionally to length, and the closure improves sharply and uniformly, which is the signature.
A blunder in one leg. Examine the closure vector against the bearing of each leg. A single bad distance or a mis-set prism constant produces a misclosure that tends to align with the offending line, and the other legs are individually consistent. Re-measure the suspect leg.
Environment and settings. Temperature and pressure errors run about 1 ppm per degree Celsius, far too small for 147 ppm; a wrong prism constant (0 versus -30 mm) is a constant, not proportional, offset. Neither fits the pattern as well as a scale problem.
Angles. Since angular closure is 18 seconds, do not spend the day re-turning angles; the evidence points to distances.
3. The party chief wants to run a compass-rule adjustment and sign the map. What do you do, and what do you tell the client?
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Do not adjust and sign. An adjustment distributes random error among the traverses in proportion to their length; it assumes the errors are random and small. Yours is neither: the angular closure shows the angles are clean, and 147 ppm is a systematic signature. Applying a compass rule would force a false closure, bend the geometry to hide a scale or blunder, and move monument positions away from their true locations. A record of survey built that way is a misrepresentation, and it is precisely the kind of thing that surfaces later in a boundary dispute or a Board complaint.
What to do: hold the map, correct or re-reduce the scale factor, re-measure the suspect leg if the pattern points to one, and reclose on the NGS monuments. Only after the closure meets 1:10,000 do you consider a least-squares or compass-rule adjustment of the residuals.
What to tell the client: the traverse fails the required closure, an adjustment cannot fix a systematic error, the map will be delayed until the closure is corrected, and the reason will be documented in writing. A missed deadline is recoverable; a knowingly false record of survey is not.